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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to add and subtract decimals. By the end of the module students should understand the method used for adding and subtracting decimals, be able to add and subtract decimals and be able to use the calculator to add and subtract decimals.

Section overview

  • The Logic Behind the Method
  • The Method of Adding and Subtracting Decimals
  • Calculators

The logic behind the method

Consider the sum of 4.37 and 3.22. Changing each decimal to a fraction, we have

4 37 100 + 3 22 100 size 12{4 { {"37"} over {"100"} } +3 { {"22"} over {"100"} } " Performing the addition, we get"} {} Performing the addition, we get

4 . 37 + 3 . 22 = 4 37 100 + 3 22 100 = 4 100 + 37 100 + 3 100 + 22 100 = 437 100 + 322 100 = 437 + 322 100 = 759 100 = 7 59 100 = seven and fifty-nine hundredths = 7.59

Thus, 4 . 37 + 3 . 22 = 7 . 59 size 12{4 "." "37 "+" 3" "." "22 "=" 7" "." "59"} {} .

The method of adding and subtracting decimals

When writing the previous addition, we could have written the numbers in col­umns.

4.37 + 3.22 ̲ 7.59

This agrees with our previous result. From this observation, we can suggest a method for adding and subtracting decimal numbers.

Method of adding and subtracting decimals

To add or subtract decimals:
  1. Align the numbers vertically so that the decimal points line up under each other and the corresponding decimal positions are in the same column.
  2. Add or subtract the numbers as if they were whole numbers.
  3. Place a decimal point in the resulting sum or difference directly under the other decimal points.

Sample set a

Find the following sums and differences.

9 . 813 + 2 . 140 size 12{9 "." "813"+2 "." "140"} {}

9.813 The decimal points are aligned in the same column. + 2.140 ̲ 11.953

841 . 0056 + 47 . 016 + 19 . 058 size 12{"841" "." "0056"+"47" "." "016"+"19" "." "058"} {}

841.0056 47.016   + 19.058   ̲

To insure that the columns align properly, we can write a 0 in the position at the end of the numbers 47.016 and 19.058 without changing their values.

Vertical addition. 841.0056 plus 47.0160 plus 19.0580 equals 907.0796. A 1 needed to be carried in the hundredths, the tens, and the hundreds columns.

1.314 - 0.58

1.314 - 0.58   ̲ Write a 0 in the thousandths position.

Vertical subtraction. 1.314 minus 0.580 equals 0.734. The ones, and hundredths digits need to be borrowed from once, and the tenths needs to be borrowed from twice to perform the subtraction.

16.01 - 7.053

16.01   - 7.053 ̲ Write a 0 in the thousandths position.

Vertical subtraction. 16.101 minus 7.053 equals 8.957. The ones, tenths, hundredths, and thousandths digits need to be borrowed from once to perform the subtraction.

Find the sum of 6.88106 and 3.5219 and round it to three decimal places.

6.88106 + 3.5219   ̲ Write a 0 in the ten thousandths position.

Vertical addition. 6.88106 plus 3.52190 equals 10.40296. A 1 needs to be carried over the tenths and ones digits to perform the addition.

We need to round the sum to the thousandths position. Since the digit in the position immediately to the right is 9, and 9>5, we get

10.403

Wendy has $643.12 in her checking account. She writes a check for $16.92. How much is her new account balance?

To find the new account balance, we need to find the difference between 643.12 and 16.92. We will subtract 16.92 from 643.12.

Vertical subtraction. 643.12 minus 16.92 equals 626.20.

After writing a check for $16.92, Wendy now has a balance of $626.20 in her checking account.

Practice set a

Find the following sums and differences.

3 . 187 + 2 . 992 size 12{3 "." "187 "+" 2" "." "992"} {}

6.179

14 . 987 - 5 . 341 size 12{"14" "." "987 - 5" "." "341"} {}

9.646

0 . 5261 + 1 . 0783 size 12{0 "." "5261 "+" 1" "." "0783"} {}

1.6044

1.06 - 1.0535 size 12{1 "." "06 - 1" "." "0535"} {}

0.0065

16,521 . 07 + 9,256 . 15 size 12{"16,521" "." "07 "+" 9,256" "." "15"} {}

25,777.22

Find the sum of 11.6128 and 14.07353, and round it to two decimal places.

25.69

Calculators

The calculator can be useful for finding sums and differences of decimal numbers. However, calculators with an eight-digit display cannot be used when working with decimal numbers that contain more than eight digits, or when the sum results in more than eight digits. In practice, an eight-place decimal will seldom be encoun­tered. There are some inexpensive calculators that can handle 13 decimal places.

Sample set b

Use a calculator to find each sum or difference.

42.0638 + 126.551

Display Reads
Type 42.0638 42.0638
Press + 42.0638
Type 126.551 126.551
Press = 168.6148

The sum is 168.6148.

Find the difference between 305.0627 and 14.29667.

Display Reads
Type 305.0627 305.0627
Press 305.0627
Type 14.29667 14.29667
Press = 290.76603

The difference is 290.76603

51.07 + 3,891.001786

Since 3,891.001786 contains more than eight digits, we will be unable to use an eight-digit display calculator to perform this addition. We can, however, find the sum by hand.

51.070000 3891.001786 ̲ 3942.071786

The sum is 3,942.071786.

Practice set b

Use a calculator to perform each operation.

4 . 286 + 8 . 97 size 12{4 "." "286 "+" 8" "." "97"} {}

13.256

452.0092 - 392.558 size 12{"452" "." "0092 - 392" "." "558"} {}

59.4512

Find the sum of 0.095 and 0.001862

0.096862

Find the difference between 0.5 and 0.025

0.475

Find the sum of 2,776.00019 and 2,009.00012.

Since each number contains more than eight digits, using some calculators may not be helpful. Adding these by “hand technology,” we get 4,785.00031

Exercises

For the following 15 problems, perform each addition or subtraction. Use a calculator to check each result.

1 . 84 + 7 . 11 size 12{1 "." "84"+7 "." "11"} {}

8.95

15 . 015 6 . 527 size 12{"15" "." "015"-6 "." "527"} {}

11 . 842 + 28 . 004 size 12{"11" "." "842"+"28" "." "004"} {}

39.846

3 . 16 2 . 52 size 12{3 "." "16"-2 "." "52"} {}

3 . 55267 + 8 . 19664 size 12{3 "." "55267"+8 "." "19664"} {}

11.74931

0 . 9162 0 . 0872 size 12{0 "." "9162"-0 "." "0872"} {}

65 . 512 8 . 3005 size 12{"65" "." "512"-8 "." "3005"} {}

57.2115

761 . 0808 53 . 198 size 12{"761" "." "0808"-"53" "." "198"} {}

4 . 305 + 2 . 119 3 . 817 size 12{4 "." "305"+2 "." "119"-3 "." "817"} {}

2.607

19 . 1161 + 27 . 8014 + 39 . 3161 size 12{"19" "." "1161"+"27" "." "8014"+"39" "." "3161"} {}

0 . 41276 0 . 0018 0 . 00011 size 12{0 "." "41276"-0 "." "0018"-0 "." "00011"} {}

0.41085

2 . 181 + 6 . 05 + 1 . 167 + 8 . 101 size 12{2 "." "181"+6 "." "05"+1 "." "167"+8 "." "101"} {}

1.0031+6.013106+0.00018+0.0092+2.11

9.135586

27 + 42 + 9 . 16 0 . 1761 + 81 . 6 size 12{"27"+"42"+9 "." "16"-0 "." "1761"+"81" "." 6} {}

10 . 28 + 11 . 111 + 0 . 86 + 5 . 1 size 12{"10" "." "28"+"11" "." "111"+0 "." "86"+5 "." 1} {}

27.351

For the following 10 problems, solve as directed. A calculator may be useful.

Add 6.1121 and 4.916 and round to 2 decimal places.

Add 21.66418 and 18.00184 and round to 4 decimal places.

39.6660

Subtract 5.2121 from 9.6341 and round to 1 decimal place.

Subtract 0.918 from 12.006 and round to 2 decimal places.

11.09

Subtract 7.01884 from the sum of 13.11848 and 2.108 and round to 4 decimal places.

A checking account has a balance of $42.51. A check is written for $19.28. What is the new balance?

$23.23

A checking account has a balance of $82.97. One check is written for $6.49 and another for $39.95. What is the new balance?

A person buys $4.29 worth of hamburger and pays for it with a $10 bill. How much change does this person get?

$5.71

A man buys $6.43 worth of stationary and pays for it with a $20 bill. After receiving his change, he realizes he forgot to buy a pen. If the total price of the pen is $2.12, and he buys it, how much of the $20 bill is left?

A woman starts recording a movie on her video cassette recorder with the tape counter set at 21.93. The movie runs 847.44 tape counter units. What is the final tape counter reading?

869.37

Exercises for review

( [link] ) Find the difference between 11,206 and 10,884.

( [link] ) Find the product, 820 10,000 size 12{"820 " cdot " 10,000"} {} .

8,200,000

( [link] ) Find the value of 121 25 + 8 2 + 16 ÷ 2 2 size 12{ sqrt {"121"} - sqrt {"25"} +8 rSup { size 8{2} } +"16" div 2 rSup { size 8{2} } } {} .

( [link] ) Find the value of 8 1 3 36 75 ÷ 2 2 5 size 12{8 { {1} over {3} } cdot { {"36"} over {"75"} } div 2 { {2} over {5} } } {} .

20 9 = 5 3  or  2 2 9 size 12{ { {"20"} over {9} } = { {5} over {3} } " or " { {2} over {9} } } {}

( [link] ) Round 1.08196 to the nearest hundredth.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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